There are numerous applications (or potential applications) in which it would be useful to transmit a laser beam over relatively long distances. For example, a laser beam transmitted through free space could be used for communication purposes. Such communications could potentially be horizontal (e.g., entirely within the atmosphere) or vertical (e.g., from ground to an orbiting satellite). As another example, laser detection and ranging (LADAR) could be used for three-dimensional imaging and mapping at long ranges. As yet another example, laser Doppler velocimetry could be useful for tracking objects over long distances.
When transmitting a laser over long distances through the atmosphere, atmospheric turbulence causes significant problems. Atmospheric turbulence leads to random fluctuations in the air density which leads to random fluctuations in refractive index. The random fluctuations in the refractive index in turn induce phase fluctuations on a laser beam propagating through turbulent air. Phase fluctuations lead to two categories of effects. The first category of effects is phase fluctuations. Over any distance, phase fluctuations degrade image quality, reducing the ability of an optical system to image through turbulence. Phase fluctuations can also degrade the ability of a communication system because the received beam must be focused onto a detector or into a single mode fiber. The second category of effects is optical scintillation. Over long propagation distances, phase aberrations lead to intensity fluctuations—referred to as scintillation. One example of scintillation is the “twinkling” of stars in the night sky. A second example is that for a laser beam propagating through turbulence, the phase aberrations along the path lead to a random de-focusing and break-up of the beam, making the beam focus poorly at the desired location. One of the phenomena associated with optical scintillation is the appearance of branch points in the phase function, which occur when the optical field has a null value due to optical scintillation. Branch points in the phase function can degrade the performance of methods that have been developed to correct for the impact of phase aberrations on systems designed for imaging and propagation through turbulence.
Various efforts have been made to develop adaptive optical (AO) systems that compensate for the effects of atmospheric turbulence on laser propagation. In general “adaptive optics” is a blanket name for technologies to improve quality of images obtained through a turbulent optical path and/or pre-compensate a laser beam for propagation through a turbulence optical path. Known AO systems have various limitations. Most known AO systems employ a Hartmann sensor to measure phase variations in a laser beam wavefront to develop commands to be applied to a deformable mirror to correct and cancel the phase aberrations. Hartmann sensor systems are incapable of correcting the branch point contribution to the phase function that is caused by strong scintillation. Other proposed systems employ a self-referencing interferometer (SRI) as a wavefront sensor. These systems generally require full “unwrapping” of the phase (i.e., calculating a phase change through numerous multiples of 2π). Moreover, the best known control system to work with SRI wavefront sensor technology requires four wavefront sensor apertures for each channel of a phase correcting device such as a deformable mirror. This results in a computational complexity on the order N2, where N is the number of phase correcting device control channels.